I'm going to go in a slightly different direction. From what you have said, I'm skeptical that you are going to like many of these suggestions. Many of the people on here, including me, smoke heavier bodied cigars than you seem to like. Fuentes were suggested earlier, and that's what I think of as a mild/medium bodied smoke, but you said you don't like Hemingways. Fuente makes a lot of other cigars, you may want to sort through them.
Ashton (also made by Fuente) is another good mild/medium smoke, but you probably want to stay away from VSG, ESG as they are stronger.
Sounds to me like you should check out more offerings by the General - RyJ, Montecristo, Hoyo de Monterrey, etc. Punch is my favorite General cigar line, but they tend to be stronger except for the regular Punch Clasico.
I also like La Aurora's stuff, and they have more mild/medium offerings (107, preferidos, etc.). You probably want to stay away from the Barrel Aged and ADN. I like them, doubt you would.
I'm sure there are more "craft" suggestions for mild/medium smokes, but I don't have any because I don't smoke them.